Lectures related to Summation Formulas of Arithmetic Functions

Explores stable laws, limit theorems, and random variable properties.

Explores well ordering, induction, Euclidean division, and prime factorization in integers.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers integration on H_pxH and arithmetic topics, focusing on the Hensel Lemma and the process of finding R and S such that R.S-P=0.

Groups and Numbers: Hidden Subgroup Problem

Explores groups and numbers, emphasizing the hidden subgroup problem and its complexities in classic and quantum algorithms.

Fourier Series: Understanding Periodicity and Coefficients

Explores t-periodic functions in Fourier series, discussing intervals, propositions, and variable changes for coefficient calculation and series convergence.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Weierstrass Preparation Theorem

Explores the Weierstrass Preparation Theorem for entire functions and the construction of root sequences.